Basic nanosystems of early 4d and 5d transition metals: Electronic properties and the effect of spin-orbit interaction

Abstract

There are various possibilities for the structure as well as for the growth of nanosystems, particularly of nanowires. The ultimate one-dimensional material—linear chains—are difficult to exploit for applications due to their transient nature. Nonetheless these are a good prototype for studying one-dimensional materials and project the kind of behavior one may expect from ultrathin nanowires. Likewise monolayers are the ultimate two-dimensional materials and their study is helpful in understanding the behavior of two-dimensional materials. We present a theoretical study on basic nanosystems—linear chains and monolayers—of the 4d (Y, Zr, Nb, Mo, and Tc) and 5d (Hf, Ta, W, and Re) transition metals of groups 3–7 by means of an all-electron density functional approach. We have explored all kinds of magnetic configurations: nonmagnetic, ferromagnetic, and antiferromagnetic, by (i) inclusion and (ii) omission of spin-orbit interaction. We find that though this interaction has a marginal effect on nanosystems of 4d transition metals, its impact becomes stronger with lowering of dimensionality. Further it has a significant effect on properties of nanosystems of 5d transition metals as well as those of bulk. It is interesting to note that the monolayers of 5d transition metals seem reluctant to order magnetically despite the general tendency of nanosystems of 4d transition metals and linear chains of 5d transition metals to woo magnetic ordering. The nanosystems with preference for antiferromagnetic ordering are found to be stable at larger nearest-neighbor distances compared to the ferromagnetic and nonmagnetic phases. Specially, antiferromagnetic monolayers of Nb and Mo are predicted to exhibit larger separations with respect to bulk, a feature observed only for some low-dimensional systems. All the monolayers, except Y, are predicted to have a nonmagnetic state almost degenerate with ferromagnetic or antiferromagnetic state. Therefore suitable substrate selection is likely to play an important role in controlling the magnetic ordering in monolayers. Interestingly, Mo linear chains are predicted to have a small energy gap at the Fermi energy, a feature not predicted for any other low-dimensional system of studied transition metals. The stable value of magnetic moment in the vicinity of the equilibrium nearest-neighbor separation for monolayers of Y and for linear chains of Zr, Mo, Tc, and Ta suggests potential of these low-dimensional systems as thermally stable nanoscale devices. Comparison with available experimental data on similar systems confirms consistency of our results. We feel that the results predicted here can be helpful guides to experimentalists as well as theorists.